dnanmeanpw.c (4362B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2020 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 #include "stdlib/stats/base/dnanmeanpw.h" 20 #include <stdint.h> 21 22 /** 23 * Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using pairwise summation. 24 * 25 * ## Method 26 * 27 * - This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`. 28 * 29 * ## References 30 * 31 * - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050). 32 * 33 * @private 34 * @param N number of indexed elements 35 * @param W two-element output array 36 * @param X input array 37 * @param stride stride length 38 * @return output value 39 */ 40 static void dnansumpw( const int64_t N, double *W, const double *X, const int64_t stride ) { 41 double *xp1; 42 double *xp2; 43 double sum; 44 int64_t ix; 45 int64_t M; 46 int64_t n; 47 int64_t i; 48 double s0; 49 double s1; 50 double s2; 51 double s3; 52 double s4; 53 double s5; 54 double s6; 55 double s7; 56 double v; 57 58 if ( N <= 0 ) { 59 return; 60 } 61 if ( N == 1 || stride == 0 ) { 62 if ( X[ 0 ] == X[ 0 ] ) { 63 W[ 0 ] += X[ 0 ]; 64 W[ 1 ] += 1; 65 return; 66 } 67 return; 68 } 69 if ( stride < 0 ) { 70 ix = (1-N) * stride; 71 } else { 72 ix = 0; 73 } 74 if ( N < 8 ) { 75 // Use simple summation... 76 sum = 0.0; 77 n = 0; 78 for ( i = 0; i < N; i++ ) { 79 v = X[ ix ]; 80 if ( v == v ) { 81 sum += X[ ix ]; 82 n += 1; 83 } 84 ix += stride; 85 } 86 W[ 0 ] += sum; 87 W[ 1 ] += n; 88 return; 89 } 90 // Blocksize for pairwise summation: 128 (NOTE: decreasing the blocksize decreases rounding error as more pairs are summed, but also decreases performance. Because the inner loop is unrolled eight times, the blocksize is effectively `16`.) 91 if ( N <= 128 ) { 92 // Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)... 93 s0 = 0.0; 94 s1 = 0.0; 95 s2 = 0.0; 96 s3 = 0.0; 97 s4 = 0.0; 98 s5 = 0.0; 99 s6 = 0.0; 100 s7 = 0.0; 101 n = 0; 102 103 M = N % 8; 104 for ( i = 0; i < N-M; i += 8 ) { 105 v = X[ ix ]; 106 if ( v == v ) { 107 s0 += v; 108 n += 1; 109 } 110 ix += stride; 111 v = X[ ix ]; 112 if ( v == v ) { 113 s1 += v; 114 n += 1; 115 } 116 ix += stride; 117 v = X[ ix ]; 118 if ( v == v ) { 119 s2 += v; 120 n += 1; 121 } 122 ix += stride; 123 v = X[ ix ]; 124 if ( v == v ) { 125 s3 += v; 126 n += 1; 127 } 128 ix += stride; 129 v = X[ ix ]; 130 if ( v == v ) { 131 s4 += v; 132 n += 1; 133 } 134 ix += stride; 135 v = X[ ix ]; 136 if ( v == v ) { 137 s5 += v; 138 n += 1; 139 } 140 ix += stride; 141 v = X[ ix ]; 142 if ( v == v ) { 143 s6 += v; 144 n += 1; 145 } 146 ix += stride; 147 v = X[ ix ]; 148 if ( v == v ) { 149 s7 += v; 150 n += 1; 151 } 152 ix += stride; 153 } 154 // Pairwise sum the accumulators: 155 sum = ((s0+s1) + (s2+s3)) + ((s4+s5) + (s6+s7)); 156 157 // Clean-up loop... 158 for (; i < N; i++ ) { 159 v = X[ ix ]; 160 if ( v == v ) { 161 sum += X[ ix ]; 162 n += 1; 163 } 164 ix += stride; 165 } 166 W[ 0 ] += sum; 167 W[ 1 ] += n; 168 return; 169 } 170 // Recurse by dividing by two, but avoiding non-multiples of unroll factor... 171 n = N / 2; 172 n -= n % 8; 173 if ( stride < 0 ) { 174 xp1 = (double *)X + ( (n-N)*stride ); 175 xp2 = (double *)X; 176 } else { 177 xp1 = (double *)X; 178 xp2 = (double *)X + ( n*stride ); 179 } 180 dnansumpw( n, W, xp1, stride ); 181 dnansumpw( N-n, W, xp2, stride ); 182 } 183 184 /** 185 * Computes the arithmetic mean of a double-precision floating-point strided array, ignoring `NaN` values and using pairwise summation. 186 * 187 * @param N number of indexed elements 188 * @param X input array 189 * @param stride stride length 190 * @return output value 191 */ 192 double stdlib_strided_dnanmeanpw( const int64_t N, const double *X, const int64_t stride ) { 193 double W[] = { 0.0, 0.0 }; 194 dnansumpw( N, W, X, stride ); 195 return W[ 0 ] / W[ 1 ]; 196 }